- #1
alpha01
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Homework Statement
Using the local minima, local maxima and points of inflection of the following function, plot the graph:
f(x) = 9x4-11x3+3x2+1
The Attempt at a Solution
f(x) = 9x4-11x3+3x2+1
f ' (x) = 36x3-33x2+6x
= 3x(12x2-11x+2)
= 3x(3x-2)(4x-1)
therefore we have x = 0, 2/3, 1/4
now, finding the second derivative of the function we have:
f '' (x) = 108x2 - 66x + 6
plugging in our values of x into this, we have:
f '' (0) = 6
f '' (2/3) = 10
f '' (1/4) = - 15/4
therefore we have local minima x = 0, 2/3
and local maxima x = 1/4
I have also found 1 point of inflection to be: 0.029...
I have plotted the function using an online function plotter, and the local minima/maxima don't appear to correspond with the actual graph.
Could someone please show in which step i went wrong?